You can also use the Add Surface Information tool, which will interpolate the elevation at each point and add the field to your data.
Nice advice, but that tool never works.
Why did you get rid the simply tool that used to be in the "3D Analyst" drop down box, "Create 3D shp" or something like that. Now you make it a multi step process.
The only way that I have seen that tool fail was when you have an existing field for what it is looking to create. I would consider renaming or removing the field with the same name it is looking to create. The only other reason that tool fails is when you have one set of data, usually the raster, that has a coordinate system and the point file is unprojected. I would consider the projection, the field names and if both are correct, then contact Esri Support.
If you are looking for the described functionality, they I recommend looking at the tool Create 3d Feature by Attribute, it should create the desired output without the 'multi-step.' The Add Surface Information tool is usually used on 2d points and allows them to determine a z.